pQCD factorization for heavy quarkonium production and fragmentation functions

From Tevatron and LHC data, it is clear that the non-relativistic QCD (NRQCD) model for heavy quarkonium production, which is the most popular one at present, is not able to explain the polarization of produced heavy quarkonia at high transverse momentum p_T. A new approach to evaluate heavy quarkonium production, expanding the cross section in powers of 1/p_T before the expansion in powers of alpha_s, was proposed recently. In terms of perturbative QCD (pQCD) factorization, it is proved that both the leading and next-to-leading power terms in 1/p_T for the cross sections can be systematically factorized to all orders in powers of alpha_s. The predictive power of this new pQCD factorization formalism depends on several unknown but universal fragmentation functions (FFs). With new QCD evolution equations for FFs, one only needs to determine these FFs at an initial scale of the order of heavy quarkonium mass. In this talk, I will introduce the framework of the new factorization method and discuss the calculation of the input FFs in NRQCD factorization model.